It was more the flavor than the texture, I think. The cookies were "medium" hardness, if that makes sense! They weren't like soft, just baked cookies. They also weren't hard like Chips Ahoy. I have no problem with Chips Ahoy, but they aren't soft.
The ice cream, if I remember correctly, wasn't like hard hand-dipped ice cream. It was pretty soft, but I don't think it was actually soft serve. It was squished between the cookies so it was hard to tell.
I just didn't care for the flavor. It tasted very "store bought". Like something I would put together at home with stuff from the grocery hoping it would taste like something from a restaurant. And since I am not that particular it is unusual for me to say I really didn't care for a dessert. I tend to be far pickier about cake than other sweets, but the Cookie Monster didn't do it for me.